This has been noted before if the Supreme's actually follow the record, they will have a tough time overturning Walker's finding:

...to Walker's surprise, after lawyers for same-sex couples put on a
parade of witnesses, gay marriage foes put on scant evidence, offering
just two witnesses, including one who later came out in favor of
same-sex marriage rights. "I did think the proponents of Proposition 8
would put on a case," Walker said.

"It never occurred to me
that they would ... ," and his trademark baritone trails off. Walker
asks for the correct baseball term for taking a swing and a miss at a
pitch and then just shrugs.

Years of legal precedent dictate that "the record" is the primary factor in determining whether a decision below is affirmed or reversed.

To reverse on this record would really require a Justice to go out of their way to actively flout how court's are supposed to work, a real bit of judicial activism.